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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 5160d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5160.l3 | 5160d1 | \([0, 1, 0, -4316, -98880]\) | \(34739908901584/4081640625\) | \(1044900000000\) | \([2]\) | \(10240\) | \(1.0377\) | \(\Gamma_0(N)\)-optimal |
| 5160.l2 | 5160d2 | \([0, 1, 0, -16816, 731120]\) | \(513591322675396/68238500625\) | \(69876224640000\) | \([2, 2]\) | \(20480\) | \(1.3843\) | |
| 5160.l1 | 5160d3 | \([0, 1, 0, -259816, 50886320]\) | \(947094050118111698/20769216075\) | \(42535354521600\) | \([2]\) | \(40960\) | \(1.7308\) | |
| 5160.l4 | 5160d4 | \([0, 1, 0, 26184, 3895920]\) | \(969360123836302/3748293231075\) | \(-7676504537241600\) | \([2]\) | \(40960\) | \(1.7308\) |
Rank
sage: E.rank()
The elliptic curves in class 5160d have rank \(0\).
Complex multiplication
The elliptic curves in class 5160d do not have complex multiplication.Modular form 5160.2.a.d
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
